Carolynne "religiously" buys everything at Tesco. Not only her groceries, but DVDs, games and anything else she can get through the supermarket. She's made her husband take out a Lloyds credit card, and buys all her petrol at Shell. The reason? So she can collect the Airmiles for a once-in-a-lifetime family holiday in Florida planned for 2013.

Gabrielle is similar. So far she's collected 7,000 miles and is not far short of the total needed to take her 18-year-old daughter to New York. But both are now furious that their plans have been left on the runway after Airmiles this week said it was stopping its current scheme, relaunching as Avios. It will charge Carolynne and Gabrielle £300 a head or more for what used to be free flights across the Atlantic.

"I am sooooo upset – it's taken away our dream," says Gabrielle. She's joined a growing backlash that has already sparked a Facebook campaign and a protest website called Fight the Airmiles Change.

Scores of disappointed Airmiles customers have vented their rage on Facebook, with Carolynne's response typical. "Because I will now have to pay the taxes, it will cost me at least the same as buying flights directly with [another] airline. Surely we should be given at least a year to collect the Airmiles we need at the present rate. I really feel cheated and would never have bothered if I knew this was going to happen," she says.

Airmiles relaunches as Avios on 16 November, and will merge with the separate loyalty programmes run by British Airways Executive Club (BA Miles) and Iberia (Iberia Plus). Emails and letters currently going out to the 2.2m members of the Airmiles scheme talk of "exciting new benefits". Customers will enjoy new flexibility when booking, while flyers from UK regional airports will no longer be charged extra miles if they have to connect through London.

A new "zone" map will make destinations such as Berlin and Prague more accessible to those who have saved a limited number of points.

But the change that has enraged many customers is that they will now have pay in cash for the "taxes, fees and charges" that airlines add on to the basic cost of a flight, and which in some cases is equal to three-quarters of the total cost.

For example, the cheapest flight from London to New York on BA in mid-November is around £400. Under Airmiles, customers needed to save up 5,000 miles for a free return flight. Under Avios, they will have to save up slightly fewer – but will have to pay the £301 a head that BA levies in taxes, fees and charges. Overnight, the value of Airmiles used on a New York flight has fallen from £400 to £100 – prompting many customers to complain they have been "robbed".

Airmiles managing director Andrew Swaffield says it had no choice but to start charging.

"I do understand fully that this increase is unwelcome, and in a perfect world we would not want to do it. But taxes, fees and charges have risen by as much as 50% -112% over the last two years alone. For example, the UK government now charges air passenger duty of £340 for a family of four travelling to Australia. France charges £15. We are not in control of these sorts of costs, and are unable to continue to subsidise that level of taxes, fees and charges."

Within Europe, Airmiles has capped the maximum fee passengers will pay at £27 per return flight. Swaffield adds that only a small percentage of Airmiles customers buy long-haul flights with their miles, with 87% going to Europe. Paris is the top destination, followed by Rome.

From November, existing Airmiles will be swapped for new Avios rewards on a 10-to-one basis. So if you have saved up, say, 1,500 Airmiles, they will be exchanged for 15,000 Avios points. Generally speaking, the amount of points you need to redeem to get to your destination has gone up 10 times as well, although some cities have become "cheaper" to get to, others more expensive.

The old "zone 1", which needed 750 miles for a flight, extended only to the UK and Ireland, Paris, Amsterdam and Brussels. Under Avios, it widens to include Berlin and Prague. But the catch is that on top of the £27 fee, customers will have to collect 9,000 Avios miles – equal to 900 Airmiles.

What's more, if the flight is not on BA or Iberia, the customer has to pay in full the taxes, fees and charges, which could add up to £100 or more.

Brian Caruana from Perthshire is one of the campaigners who helped launch the fighttheairmileschange.co.uk website. He collects around 7,000-8,000 Airmiles a year, and is incensed that as recently as this month he has been sent promotional material by Airmiles encouraging him to pay cash to top up his total.

"I feel robbed," he says. "Can't they just freeze the entitlements that people have saved up? Or offer a better rate of exchange to Avios points? Or extend the period in which we can redeem flights without having to pay taxes, fees and charges? You can see why so many people will be saying Adios to Avios."

On the site, angry customers allege that Airmiles is in breach of contract for selling miles for cash that will now be devalued. Others believe the change falls foul of the unfair terms in contracts regulations.

This week Caruana emailed the head of every company that partners Airmiles, including Tesco, Shell, Lloyds, John Lewis, Avis, eBay and Play.com – to urge them to put pressure on Airmiles to reconsider. Lloyds told Money it was aware that some of its credit card customers are disgruntled by aspects of the change, but that it stands by the deal.

Airmiles customers will now have until 14 November (booking online) or 15 December (booking by phone) to redeem their Airmiles without having to pay taxes, fees and charges. So long as customers book by then, they will be able to choose a free flight up to December 2012.

Expect many of the best seats and destinations to book up fast as customers flock to unload their miles. If you have 1,500 Airmiles, a couple can still get free flights for a spring weekend in Paris next year. But after November that will cost the equivalent of 1,800 miles plus £54. Book now before the rush …

Pros and cons of the new scheme

Cons

• Previously free long-haul flights will cost as much as £500 in taxes, fees and charges

• Previously free BA and Iberia European flights will carry a £27 fee

• Passengers of all flights not operated by IAG (BA and Iberia) will pay full taxes, fees and charges

• Some popular routes, such as Paris, will require more Airmiles

Pros

• 70% of routes will require fewer miles

• Flyers will be able to buy one-way flights for first time

• No more supplements for flyers from UK regional airports

And what Facebook protesters are saying

Ann Bradshaw: I have been collecting Airmiles for years and years. I have a Tesco credit card on which I collect Airmiles and use it to pay for absolutely everything I can. I also shop at Tesco when I can and have it all converted automatically into Airmiles. In July 2011 I had enough miles to fly to Trinidad (6,500 Airmiles) for a holiday so the holiday was completely free after years and years of collecting. I am now told that I will need 50,000 Avios and £301 to pay in taxes if I want to do the same journey again! I was gob smacked! Goodbye Airmiles – it is no longer worth my while. I shall collect Nectar points and go to Alton Towers for my holidays instead!

Olaf Searson, 28, from Chudleigh, Devon: I have been collecting Airmiles for a few years. I'm not a big spender, but I managed to save up enough Airmiles by November 2010 to go to Belfast for a long weekend as a birthday treat. I used a little over 2,000 Airmiles for the flight and part payment towards a hotel – 750 of those miles were for the flight from Exeter, which was totally free. Since November 2009 I have converted around £110 in Tesco Clubcard vouchers alone (by my calculations that's 11,000 Clubcard points, or at the x2 rate, £5,500 spent in Tesco). I even used Tesco to get four new tyres through Tesco Tyres. The cost was £40 more than the cheapest quote I got, but I thought the benefit of having the extra Clubcard points outweighed the cost saving using the other supplier.

I feel cheated by the change. Airmiles have told be it's "exciting" but I fail to see how. Sure, regional supplements have been reduced. Until you read the small print and see that this is only for flights on BA or Iberia.

If I want to take the same flight to Belfast from Exeter, I would have to use more miles (9,000 under the new scheme) and to stump up about £100 for taxes, surcharges and other charges as Flybe is not a member of IAG group. That's a flight that previously was free, using fewer miles.

I feel that my loyalty and custom to these brands has been for nothing.